1. Field of the Invention
The present invention relates to a band pass filter which is a high order band pass filter obtained by series connecting plural secondary band pass filters having different center frequencies and can change its characteristics.
2. Description of the Related Art
Band pass filters used for various signal processing devices are often constructed of analog circuits, and most of them are used in such a state that characteristics (that is, maximum gain, band width, and center frequency) of the band pass filter are fixed.
FIG. 5 is a view showing the characteristics of a general second order band pass filter.
In the drawing, ω0 denotes a center frequency, G0 denotes a maximum gain, and ωb denotes a band width.
Some band pass filters can vary their characteristics by using characteristic variable parts (that is, parts for making the characteristics of the band pass filter variable) such as variable resistors and variable capacitors, or by using a resistance variable technique by switching of switched capacitors, switched resistors or the like.
The characteristic variable part is often used for a device in which the characteristics of the band pass filter is manually changed (for example, a device in which a tuning frequency is manually changed by using the band pass filter constructed of a coil and a variable capacitor) or for finely adjusting the frequency characteristic variation and error of the band pass filter.
In the case where the resistance variable technique by switching is used, since the characteristics can be changed using a control signal from the outside, such as a frequency, the band pass filter can be applied to a device in which characteristics are automatically changed according to a control condition or the like.
Besides, when the resistance variable technique by switching of the switched capacitor, the switched resistor or the like is used, it becomes possible to change the characteristics by a control signal (that is, a switching frequency) from the outside, a single circuit structure can support many frequencies, and there are obtained great effects such as reduction in cost by commonality of parts.
From these, the band pass filters which can vary the characteristics are used for many signal processing devices.
A specific example of a second order band pass filter which can vary a specified band pass filter characteristic (characteristic of one of maximum gain, band width and center frequency) will be described.
As such a band pass filter, a multiple feedback circuit (also called a friend circuit) shown in FIG. 6 and a biquad circuit shown in FIG. 7 are common.
In FIGS. 6 and 7, R1, R2, R3, . . . denote fixed resistors, C1, C2, . . . denote capacitors, and OP1, OP2 . . . denote operational amplifiers.
For example, in the case where a second order band pass filter which can vary filter characteristics is constructed by using the multiple feedback circuit shown in FIG. 6, for example, when the resistor R2 is made a variable resistor, only the center frequency can be made variable. This can be explained from the transfer function of the multiple feedback circuit.
The transfer function of this circuit is given byG(s)=−(1/(R1*C2))*s/(s^2+((C1+C2)/(C1*C2*R3))*s+1/(R3*C1*C2)*(1/R1+1/R2))),and the respective characteristics (maximum gain (G0), band width (ωb), and center frequency (ω0)) are expressed by following expressions. Incidentally, “^” of s^2 means a power (involution), and s^2 means s2.G0=(C1*R3)/((C1+C2)*R1)ωb=(C1+C2)/(C1*C2*R3)ω0=sqrt(1/(C1*C2*R3)*(1/R1+1/R2)))
Incidentally, sqrt( )=√{square root over ( )}, and sqrt(A) means the square root of A (the same shall apply hereinafter).
That is, sqrt(1/(C1*C2*R3)*(1/R1+1/R2)) means {[1/(C1*C2*R3)]*(1/R1+1/R2)}1/2.
From the above expressions, since R2 has an influence on only the center frequency characteristic, when only R2 can be made variable, only the center frequency can be made variable.
On the contrary, in the case where an element other than R2 is made variable, the respective characteristics are influenced.
In the case where a second order band pass filter which can vary filter characteristics is constructed by using the biquad circuit shown in FIG. 7, when the resistor R1 is made a variable resistor, only the maximum gain can be made variable, and when one of the resistors R3, R4, R5 and R6 is made a variable resistor, or C2 is made a variable capacitor, only the center frequency can be made variable.
This can also be explained from the transfer function of the biquad circuit.
The transfer function of this circuit is given byG(s)=(1/(R1*C1))*s/(s^2+(1/(C1*R2))*s+R6/(C1*C2*R3*R4*R5)),and the respective characteristics (maximum gain (G0), band width (ωb), and center frequency (ω0)) are expressed by following expressions.G0=R2/R1ωb=1/(C1*R2)ω0=sqrt(R6/(C1*C2*R3*R4*R5)
From the above expressions, since R1 has an influence on only the maximum gain, and R3, R4, R5, R6 and C2 have an influence on only the center frequency characteristic, when these resistors or capacitance can be made variable, only the maximum gain and the center frequency can be made variable.
Also in the case of the biquad circuit, in the case where an element other than R1, R3, R4, R5, R6 and C2 is made variable, the respective characteristics are influenced.
When such a circuit is used, the filter characteristic can be made variable by making a specified element of the band pass filter variable.
Besides, as a method of making a specified element variable, as described above, there is a method of using a characteristic variable part such as a variable resistor and a variable capacitor, or a resistance variable technique using a switched capacitor or a switched resistor which makes a resistance value variable by switching.
Next, also with respect to the switched capacitor and the switched resistor, specific examples will be described.
FIG. 8 is a model diagram of the switched capacitor.
In the case where a switch Sc is switched at a frequency fCLK, a current flowing through a capacitor C is expressed byic=C*(Vin−Vout)/TCLK=C*fCLK*(Vin−Vout).
When the switched capacitor is written as an equivalent resistance Rc,Rc=(Vin−Vout)/ic=1/(C*fCLK).
The above expression indicates that the equivalent resistance Rc is obtained by switching on and off the capacitor C at a frequency fc.
FIG. 9 is a model view of the switched resistor.
In the case where a switch Sr is switched on and off at an off duty α%, a current flowing through a resistor Rb is expressed by, when consideration is given to the fact that the current flows only hen the switch Sr is switched off,ir=α*Vin/(Ra+Rb).
When the switched resistor is written as an equivalent resistance Rr,Rr=Vin/ir=(Ra+Rb)/α
The above expression indicates that the equivalent resistance Rr is obtained by switching on and off the resistors Ra and Rb at the off duty α%.
In the second order band pass filter as described above, when the switched capacitor or the switched resistor is used as the resistor for making the filter characteristic variable, the filter characteristic of the band pass filter can be made variable by a control signal (frequency signal) from the outside.
That is, in the case of the switched capacitor shown in FIG. 8, the frequency signal indicated by fCLK(1/TCLK) is the control signal from the outside, and in the case of the switched resistor shown in FIG. 9, the frequency signal indicated by fCLK(1/TCLK) is the control signal from the outside.
The equivalent resistance value can be changed by changing the frequency of the control signal from the outside.
In general, an object of using a signal processing device with such a band pass filter is
to extract (amplify) only a signal component of a required frequency band, and
to attenuate a signal in a frequency band other than that.
However, since the filter characteristics of the second order band pass filter other than the maximum gain are theoretically determined by only the center frequency and the band width, there is a case where objective frequency characteristics can not be obtained.
For example, in the case where noise is mixed in the vicinity of the required frequency band, there has been a case where a noise removal effect can not be sufficiently obtained.
In this case, the characteristics are often improved by using a high order band pass filter obtained by series connecting the second order band pass filters.
In the case where a fourth order band pass filter is obtained by series connecting two band pass filters, there are generally two kinds of systems, that is, a single tuning system in which the second order band pass filters having identical center frequencies are series connected, and a stagger tuning system in which the second order band pass filters having different center frequencies are series connected.
FIG. 10 is a view showing filter characteristics in the case of the single tuning system, and FIG. 11 is a view showing filter characteristics in the case of the stagger tuning system.
First, consideration will be given to a case where the respective characteristics of the fourth order band pass filter of the single tuning system are made variable. In the single tuning system, when the band width of each of the pair of the second order band pass filters is kept fixed and the maximum gain of at least one of them is changed, the maximum gain of the whole of the fourth order band pass filter is changed.
When the band width of each of the pair of the second order band pass filters is kept fixed and the center frequencies of the respective second order band pass filters are made variable while the center frequencies have the same value, the centre frequency of the fourth order band pass filter can be made variable while the band width thereof is fixed.
That is, in the case of the single tuning system, the high order band pass filter can be easily made variable by the foregoing conventional method.
However, in the case of the single tuning system, also as shown in FIG. 10, in the case where the attenuation characteristic at a skirt part is desired to be enhanced, the steepness in a passing region becomes high, and it has been difficult to widen the band width. On the contrary, in the case where the band width is desired to be widened, it has been difficult to enhance the attenuation characteristic at the skirt part.
On the other hand, when the stagger tuning system is used, even if the attenuation characteristic at the skirt part is enhanced, the band width can be widened, and the flatness in the band can also be enhanced.
Accordingly, in order to extract a signal component of a required frequency band, the stagger tuning system is often more advantageous than the single tuning system.
The foregoing related art is disclosed in non-patent document 1 set forth below, and for example, the features of the biquad circuit and the transfer function are detailed in Chapter 5, the stagger tuning is detailed in Chapter 7, and the switched capacitor is detailed in Chapter 17.
Non-patent document 1 (Japanese version)
Design of Analog Filter [Author: M. E. VAV VALKENBURG Translator: Hajime Kanai Publisher: Kabusiki Kaisha Sangyo Houchi Center Publication of first edition: Mar. 25, 1985]
Non-patent document 1 (English version)
Analog Filter Design [Author: M. E. VAV VALKENBURG Publisher: CBS College Publication: 1982]
However, in the stagger tuning system, in the case where the characteristic of the fourth order band pass filter is made variable in the state where the band width is fixed, it is necessary that the difference (offset) between the center frequencies of the respective second order band pass filters is fixed, and the respective center frequencies are made variable.
In order to make the center frequencies of the pair of the second order band pass filters variable while the offset of the center frequencies is fixed, in both the case of the multiple feedback type and the biquad type, the calculation of resistance values for determining the center frequency, the maximum gain or the like becomes complicated.
Thus, in the case where variable resistors or the like are used, in order to keep the band width of the fourth order band pass filter constant, it is necessary that the center frequency adjusting resistors of the respective second order band pass filters are separately adjusted to target resistance values.
Besides, in the fourth order band pass filter, when only the center frequency is changed by using a switched capacitor or the like and by changing a resistance value by a control signal from the outside, it is necessary to separately give control signals (fCLK) having different frequencies to the switched capacitors of the two second order band pass filters, and there has been a problem that a circuit scale becomes large.